NEW ASYMPTOTIC LAW GOVERNING OVERALL TEMPORAL CORRELATIONS IN CHAOTIC SYSTEMS - ENSEMBLE HOMOGENIZATION AND ORDER-Q POWER SPECTRUM

A new statistical-physical asymptotic law relevant to explicit correlation in temporal fluctuations generated by chaotic dynamics is found. Homogenizing the ensemble members, we can introduce the order-q power spectrum I(q)(omega) in the "thermodynamic" limit, whose poles are proved to be determined by the eigenvalues of the order-q evolution operator H(q) previously introduced. It is a natural extension of the conventional power spectrum I(omega)( = I(q) = 0(omega)), and enables us to study various correlation characteristics by controlling the value of parameter q. This manifests that the intensive variable q governs overall temporal-correlation characteristics as well as the global aspect described by fluctuation-spectrum theory.